Grace McCourt

activity

20202023

most citedLinear Bounds for Cycle-free Saturation Games

2 citations · 3 across the 8 of their papers we have counts for

collaborators

Showing 2022Show all

4 papers · 1 filter

math.CO2022

A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs

Alexandr Kostochka, Ruth Luo, Grace McCourt

Dirac proved that each $n$ -vertex $2$ -connected graph with minimum degree at least $k$ contains a cycle of length at least $min {2 k, n}$ . We consider a hypergraph version of this…

math.CO2022

On a property of $2$ -connected graphs and Dirac's Theorem

Alexandr Kostochka, Ruth Luo, Grace McCourt

We refine a property of $2$ -connected graphs described in the classical paper of Dirac from 1952 and use the refined property to somewhat shorten Dirac's proof of the fact that eac…

math.CO2022

Minimum degree ensuring that a hypergraph is hamiltonian-connected

Alexandr Kostochka, Ruth Luo, Grace McCourt

A hypergraph $H$ is hamiltonian-connected if for any distinct vertices $x$ and $y$ , $H$ contains a hamiltonian Berge path from $x$ to $y$ . We find for all $3 \leq r < n$ , exact lower…

math.CO2022★ 1 cited

Ramsey-Turán Problems with small independence numbers

József Balogh, Ce Chen, Grace McCourt +1

Given a graph $H$ and a function $f (n)$ , the Ramsey-Turán number $R T (n, H, f (n))$ is the maximum number of edges in an $n$ -vertex $H$ -free graph with independence number at most $f(n…

A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs

On a property of 2-connected graphs and Dirac's Theorem

Minimum degree ensuring that a hypergraph is hamiltonian-connected

Ramsey-Turán Problems with small independence numbers

On a property of $2$ -connected graphs and Dirac's Theorem